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Unit
13
COORDINATE GEOMETRY
You are familiar with locating
a point in a plane and using
coordinates to describe the
position of a point in a plane.
These coordinates are called the
Cartesian coordinates of the point.
(The name comes from the French
mathematician Rene Descartes
(1596 −1650). The system of using
a pair of coordinates to describe
the position of a point in a plane
is called Coordinate Geometry or
Cartesian Geometry.
The coordinates measure the
displacement (+ or −) of the point
from two perpendicular axes, the
y-axis (Oy) and the x − axis (Ox)
where O is the origin.
In this unit, you are going to learn
how to solve problems involving
straight lines in an x − y plane.
You will learn how to calculate the
distance between two points on a
straight line, how to nd the equation
of a straight line, and nally you will
learn to describe the condition for two
lines to be parallel and how to nd
the midpoint of a line segment.
Coordinate Geometry is applied in
many situations. For example by
recognising the relationship between
two variables, you can learn more
about real life situations and make
reasonable predictions about future
trends such as those concerning
populations and business.
Calculating the distance
between two points on a
straight line
We can represent the position of
a point with respect to the y axis
and x axis by two numbers called
coordinates. It is for this reason
that the xy-plane is also called the
coordinate plane. These numbers
are enclosed in brackets and the rst
number in the brackets represents the
position of a point with respect to the
x-axis and the second number in the
brackets represents the position of a
point with respect to the y- axis.
If we want to nd the distance
between two points on the coordinate
plane, then a simple right angled
triangle can be constructed with sides
parallel to the axes.